Science Watch; Largest Known Prime

Published: March 31, 1992

Mathematicians using a supercomputer have advanced the quest of a 17th-century French monk by discovering the largest known prime number.

The number begins 174 135 906 820 087 097 325 and goes on and on and on for 227,832 digits, filling 32 pages of computer paper. It is a prime number because it can only be divided by 1 and itself. Smaller examples of primes are 1, 2, 3, 5, 7 and 11.

"It looks like lots and lots of digits," said David Slowinski of Cray Research in Chippewa Falls, Wis., who wrote the program that led to the discovery.

And this is no ordinary prime number, but a Mersenne prime. "There are billions and billions of prime numbers," Dr. Slowinski said, but this is only the 32d Mersenne prime ever found.

Mersenne primes are named after Father Marin Mersenne, who found a few before his death in 1648. A Mersenne prime is one that fits a particular formula devised by Mersenne, and it comes with a bonus: it can be used to calculate a perfect number, one for which all the factors add up to the number. An example is 6; its factors are 1, 2 and 3. The perfect number associated with the latest prime has 455,633 digits.

The discovery was made on a Cray supercomputer at the Harwell Laboratory of AEA Technology near Oxford, England. Dr. Slowinski said he and his program have held the largest-prime record since 1979.

Jeffrey Lagarias, a mathematician at A.T.& T. Bell Laboratories in Murray Hill, N.J., said that the discovery might have some significance in pure number theory but that "it's not going to revolutionize anything."

But because the program requires intense calculation and because the answer can be readily checked, the program is used to test supercomputers, Dr. Slowinski said.

In the case of the new prime, the computer multiplied 2 by itself 756,839 times and subtracted 1.